Early T-cell activation is selected by evolution to discriminate a few foreign peptides rapidly from a vast excess of self-peptides, and it is unclear in quantitative terms how this is possible. We show that a generic proofreading cascade supplemented by a single negative feedback mediated by the Src homology 2 domain phosphatase-1 (SHP-1) accounts quantitatively for early T-cell activation, including the effects of antagonists. Modulation of the negative feedback with SHP-1 concentration explains counterintuitive experimental observations, such as the nonmonotonic behavior of receptor activity on agonist concentration, the digital vs. continuous behavior on certain parameters, and the loss of response for high SHP-1 concentration. New experiments validate predictions on the nontrivial joint dependence on binding time and concentration for the relative effect of two antagonists: We explain why strong antagonists behave as partial agonists at low concentration and predict that the relative effect of antagonists can invert as their concentrations are varied. By focusing on the phenotype, our model quantitatively fits a body of experimental data with minimal variables and parameters.